Your average person won't gain any specific benefit from that knowledge (at least when framing it in the way you're suggesting). Societally, people know exactly what you mean when you say "bird" and they know exactly what you mean when you say "dinosaur." There's a distinction between the two in every day discussions, pop-culture, in the modern dictionary, etc. And to claim otherwise is really pedantic. If Planet Zoo were to get a "dinosaur" DLC it wouldn't be a bunch of modern day birds because that would confuse people.
That said, most people at this point know that birds are descended from dinosaurs so that's something that I do raise pretty frequently (and I raise in fascination every time i see certain movements in birds).
We should be encouraging a change in thinking. Knowledge evolves.Culturally, the term "Dinosaur" has filled the catch all for almost everything Extinct, with a focus on big, scaled beasts. Prehistoric and Megafauna have been pushed occasionally, though each has their own boundaries of course. Dinosaur is the easier term for a child to say, so it's an uphill battle.
Saying "Birds are Dinosaurs" is always going to be seen as a contradiction to the majority of people (at least for a few more decades I think), in many minds being pretty close to "Birds are Dragons".
To me it's no different than discouraging differentiation between humans and animals. There is no difference, we are animals. Drawing that hard line between them is literally what has led to our modern society behaving so callously towards nature (you can actually blame the church for that, but anyway). That is why I think it's important that society as a whole adapts to new understanding of things. Likewise, who better to pick up on the new knowledge quickly than children, who don't yet have a biased frame of reference?
Insisting on there being a tangible difference between dinosaurs and birds is as ludicrous as insisting that scientists have "ruined dinosaurs" by revealing a lot of them probably had feathers. We know better now.